Answer:
Solution given:
equation is:
x²-40x+A=0
when A=200
equation becomes
x²-40x+200=0
Comparing above equation with ax²+bx+c=0 we get
a=1
b=-40
c=200
By using quadratic equation formulax=[tex]\displaystyle \frac{-b±\sqrt{b²-4ac}}{2a}[/tex]
substituting value
x=[tex]\displaystyle \frac{-*-40±\sqrt{(-40)²-4*1*200}}{2*1}[/tex]
x=[tex]\displaystyle \frac{40±\sqrt{800}}{2}[/tex]
x=[tex]\displaystyle \frac{40±20\sqrt{2}}{2}[/tex]
taking positive
x=[tex]\displaystyle \frac{40+20\sqrt{2}}{2}[/tex]
x=34.14
taking negative
x=[tex]\displaystyle \frac{40-20\sqrt{2}}{2}[/tex]
x=5.86
x=34.14 or 5.86A force of 18 lb is required to hold a spring stretched 8 in. beyond its natural length. How much work W is done in stretching it from its natural length to 10 in. beyond its natural length
Answer: 18.75 lb.ft
Step-by-step explanation:
Given
Force required to stretch spring 8 in. is 18 lb
it can be written
[tex]\Rightarrow F=kx\\\Rightarrow 18=k(8)\\\\\Rightarrow k=\dfrac{18}{8}=\dfrac{9}{2}\ lb/in.[/tex]
Work done in stretching from its natural length to 10 in.
[tex]\Rightarrow W=\dfrac{1}{2}kx^2\\\\\Rightarrow W=0.5\times \dfrac{9}{2}\times (10)^2\\\\\Rightarrow W=225\ lb.in.\ or\\\Rightarrow W=18.75\ lb.ft[/tex]
Michael is cutting logs. He has 3 logs. Michael will cut each log by. Determine the
number pieces of wood that Michael will have.
Answer:
Micheal will have 6 logs.
Step-by-step explanation:
Each log will divide into two pieces,so.
3×2= 6
Please help explanation if possible
Answer:
18.84 feet. let me know if you have ay other questions.
Step-by-step explanation:
The way to find the formula for circumference is kinda complicated so it is best to ust memorize the formula, which is 2πr. or 2 times pi times the radius.
Your problem gives you the formula, but instead of 2 and r in it you have d, which is the diameter.
The diameter of the circle is 2 times the radius, so that's why it is replaced.
the radius is the distance from the center fo the circle to one edge, and the diameter is the distance through the circle passing through its center. so it's the center to one end plus the center to another end. or r+r which is also 2r.
So d = 2r, so in this problem d =6 feet.
So now the formula πd = 3.14*6 feet = 18.84 feet
The Susan B. Anthony dollar has a radius of 0.52 inches. Find the area of one side of the coin to the nearest
hundredth.
Answer:
0.85 in²
Step-by-step explanation:
really ? you need help with that ? you could not find the formula for the area of a circle on the internet and type it into your calculator ? I can't do anything else here.
a circle area is
A = pi×r²
r being the radius.
and pi being, well, pi (3.1415....)
r = 0.52 in
so,
A = pi×0.52² = pi×0.2704 = 0.849486654... in²
the area of one side of the coin is 0.85 in²
complete the square to form a true equation;
x^2-2x+__=(x-__)^2
Answer:
see explanation
Step-by-step explanation:
To complete the square
add ( half the coefficient of the x- term )² to x² - 2x
x² + 2(- 1)x + 1
(x² - 2x + 1 = (x - 1)²
Arrange 3/5,5/8,5/6 and 7/4 in ascending order
It’s already in ascending order.
3/5= .6
5/8= .625
5/6= .833
7/4= 1.75
WILL GIVE 25 POINTS FOR ANSWERING AND BRAINIER!!!
Which answer choice correctly complete the sentence?
Asking the “Did you Check” questions is an important step in the Problem Solving Plan because you can
A. determine if your answers are reasonable.
B. organize your thoughts.
C. understand the problem better.
D. define your strategy easier.
Answer:
A
Step-by-step explanation:
It just makes the most sense
What are the x-intercepts for the function ƒ(x) = -x(x − 4)?
A 0
B -1, 4
C 4
D 0, 4
What are the solutions to the quadratic equation 4x2 − x − 3 = 0?
Answer:
D
Step-by-step explanation:
f(x)=-x(x-4)
f(x)=-x²+4x
-x²+4x=0
x(-x+4)=0
x=0, x=4
(2)
4x²-x-3=0
(4x²+3x)-(4x-3)=0
x(4x+3)-1(4x+3)=0
x=1, x=-3/4
An exponential function f(x) = ab^xpasses through the points (0, 2) and (3, 54). What are the values of a and
b?
a=
b =
Answers:
a = 2
b = 3
=======================================================
Explanation:
Plug in x = 0 and y = 2 to find that
y = a*b^x
2 = a*b^0
2 = a*1
2 = a
a = 2
Then plug in x = 3 and y = 54 to determine the value of b
y = a*b^x
y = 2*b^x
54 = 2*b^3
2b^3 = 54
b^3 = 54/2
b^3 = 27
b = (27)^(1/3)
b = 3
So we have y = a*b^x update to y = 2*3^x
190 of 7
6 7 8 9 10
-3
4
5
6
The slope of the line shown in the graph is
and the intercept of the line is
Answer:slope 2/3
Y-int 6
Step-by-step explanation:
The principal amount of money for this loan is $9,500.00. If you deposit this into an account paying 4.2% annual interest compounded monthly. How much money will be in the account after 5 years? (also called Future value).
9514 1404 393
Answer:
$11,715.65
Step-by-step explanation:
The applicable formula is ...
FV = P(1 +r/n)^(nt)
where principal P earns interest at rate r compounded n times per year for t years.
FV = $9500(1 +0.042/12)^(12·5) = $9500(1.0035^60) ≈ $11,715.65
The account will hold $11,715.65 after 5 years.
The temperature in Kansas City varies greatly some days. One day in January, the temperature was 16 degrees but then the temperature decreased by 23 degrees by midnight. What was the temperature at midnight?
Answer:
-7 degrees
Step-by-step explanation:
the temperature was 16 degrees then was the decrease by 23 degrees so subtract 23 from 16 and the answer is -7
A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 66 types of drinks to choose from, 33 types of sandwiches, and 44 types of chips. How many different value meal packages are possible
36 different value meal packages are possible
Step-by-step explanation:
To answer this question, multiply all given numbers together.
4*3*3
12*3
36
Let T:R²->R² be a linear transformation ,and assume that T (1,2)=(-1,1) and T(1,-1)=(2,3)
compute T(3,3) pls help me
Answer:
(-4,-1)
Step-by-step explanation:
We are given T(1,2)=(-1,1) and T(1,-1)=(2,3) and T is a linear transformation.
This implies for scalars a and b that
T(a(1,2)+b(-1,1))=aT(1,2)+bT(-1,1)
T((a,2a)+(-b,b))=a(-1,1)+b(2,3)
T((a-b,2a+b))=(-a,a)+(2b,3b)
T((a-b,2a+b))=(-a+2b,a+3b)
This means we should be able to solve the system below to find a and b for T(3,3):
a-b=3 and 2a+b=3
Add equations to eliminate b and solve for a:
3a=6
Divide 3 on both sides:
a=2
If a-b=3 and a=2, then b=-1.
Plug in a=2, b=-1:
T((a-b,2a+b))=(-a+2b,a+3b)
T((2--1,2×2+-1)=(-2+2×-1,2+3×-1)
T(3,3)=(-4,-1).
Factorize:
3a^2 + 10a + 3
Answer: (3a + 1) (a + 3)
Step-by-step explanation:
Concept:
Here, we need to know the idea of factorization.
It is like "splitting" an expression into a multiplication of simpler expressions. Factoring is also the opposite of Expanding.
Solve:
Given = 3a² + 10a + 3
STEP ONE: separate 3a² into two terms
3a
a
STEP TWO: separate 3 into two terms
3
1
STEP THREE: match the four terms in ways that when doing cross-multiplication, the result will give us 10a.
3a 1
a 3
When cross multiply, 3a × 3 + 1 × a = 10a
STEP FOUR: combine the expression horizontally to get the final factorized expression.
3a ⇒ 1
a ⇒ 3
(3a + 1) (a + 3)
Hope this helps!! :)
Please let me know if you have any questions
What is the extreme value of the polynomial function f(x)= x2 - 4?
Answer:
+∞.
Step-by-step explanation:
That would be positive infinity.
The extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.
What is extreme value of a polynomial?Extreme values of a polynomial are the peaks and valleys of the polynomial—the points where direction changes.
What are the steps of finding the extreme value of any polynomial?The following steps which are required to find the extreme value of polynomial are:
Arrange the polynomial into the the form of [tex]ax^{2} +bs+c[/tex] where a, b and c are numbers.Determine whether a, the coefficient of the [tex]x^{2}[/tex] term, is positive or negative.If the term is positive, the extreme value will be the infinity because the value will continue to grow as x increases.If it is negative, use the formula [tex]\frac{-b}{2a}[/tex] to find the value for extreme. And then plug [tex]x = \frac{-b}{2a}[/tex] in the original polynomial to calculate the extreme value of the polynomial.According to the given question.
We have a polynomial
[tex]f(x) = x^{2} -4[/tex]
Since, in the given polynomial the coefficient of [tex]x^{2}[/tex] is positive . Therefore, the extreme value of the given polynomial is infinity because the value will continue to grow as x increases.
Hence, the extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.
Find out more information about extreme value of a polynomial here:
https://brainly.com/question/16597253
#SPJ2
Please Answer This!!! I NEEEDDD TOOO KNOWWWWW ANSWER!!!
Answer:
77.5
Step-by-step explanation:
Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B
Which number line represents the solutions to 1-2x = 4?
Answer:
The third choice down
Step-by-step explanation:
|-2x| = 4
There are two solutions, one positive and one negative
-2x = 4 and -2x = -4
Divide by -2
-2x/-2 = 4/-2 -2x/-2 = -4/-2
x = -2 and x = 2
Make x the subject
5y + 2x = 25
Answer:
x = -5/2 y +25/2
Step-by-step explanation:
5y + 2x = 25
Subtract 5y from each side
5y + 2x -5y= -5y+25
2x = -5y +25
Divide by 2
2x/2 = -5y/2 +25/2
x = -5/2 y +25/2
Ivan invests $5,000 into an account with a 3.5% interest that is compounded semi-annually.
How much money will he have in this account if he keeps it for 15 years?
9514 1404 393
Answer:
$8414
Step-by-step explanation:
The compound interest formula is useful for this.
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r compounded n times per year for t years. A is the ending balance.
A = $5000(1 +0.035/2)^(2·15) = $5000·1.0175^30 ≈ $8414.00
Ivan will have $8414 in his account after 15 years.
What is the name of this prism?
A. trapezoidal prism
B. pentagonal prism
C. sphere
D. hexagonal prism
Can someone help me? I figured out part B however, I am struggling with part A and I would be so happy if any of you helped me. Thank you for your help.
Note: you may need to delete the comma
============================================================
Explanation:
The info "5 months" is never used to compute the mean. We could easily replace it with "6 months" or "7 months" or any stretch of time, and still get the same answer. So we'll ignore this value.
What we'll do is add up the 21 items given to us, and then divide by 21.
Because there are so many values, and it's easy to get lost, I'm going to add up across the rows
Row One: 256,229+253,657+218,747+246,163+235,626+288,694 = 1,499,116 Row Two: 316,265+196,721+319,620+285,077+215,152+253,291 = 1,586,126 Row Three: 315,011+199,901+265,443+291,806+303,556+215,359 = 159,1076 Row Four: 258,554+293,658+289,935 = 842,147Those subtotals then add up to this
1,499,116+1,586,126+1,591,076+842,147 = 5,518,465
This is the same as adding up all 21 values.
Finally, we divide that sum over 21 as there are 21 values in this list
(5,518,465)/21 = 262,784.047619048
That value then rounds up to 262,785
If your teacher just wanted things to the nearest whole number (without rounding up), then the answer would be 262,784
Side note: using a spreadsheet program would probably be the most efficient/fastest method for this type of problem.
Can someone help me with this plz
Answer:
170.7
Step-by-step explanation:
We are aware that the base is a square, with side lengths 8cm, and we are given that the height is 8 cm. Since the volume of a square based pyramid is 1/3 x base area x height, we receive 1.3 x 64 x 8 which is 512/3 which is in turn 170.666 recurring. However, since this question asks you to round the the nearest tenth, you get 170.7
At the end of 2 years, P dollars invested at an interest rater compounded annually increases to an amount, A dollars, given by the following formula.
A = P(1+r)?
Find the interest rate if $192 increased to $363 in 2 years. Write your answer as a percent..
-
Annual compound interest rate = % (Type an integer or a decimal.)
Answer:
37.5%
Step-by-step explanation:
A=P(1+r)^t
363=192*(1+r)^2
1.375=1+r, r=0.375=37.5%
in a 5 liter milk jar water and milk are in the ratio 2:3. If 1 liter of milk and 1 liter of water is added. what will be the new ratio.
Give me answer with steps . and the answer is 3:4. but how I want to know
Answer:
ratio of water and milk=2:3
i.e. water=2
milk=3
now adding 1 liter of water in 2
2+1=3
and 1 liter of milk in 3
3+1=4
hence,
the new ratio is 3:4
Step-by-step explanation:
i hope this will help
plz mark as brainliest
NEED HELP ASAPPPPP !!!
Answer:
2160
Step-by-step explanation:
because c is 15 and d is 12 therefore d² is 144 and 144x15 is 2160
Answer:
2160
Step-by-step explanation:
Substitute
[tex](15)(12) {}^{2} [/tex]
[tex]15 \times 144 = 2160[/tex]
Five subtracted from seven times a number is 9. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is _____________
B) Solve your equation in part [A] for
Answer:
x=
Answer:
18
Step-by-step explanation:
7-5=2
2x9=18
Carol is having a hard time understanding the central limit theorem, so she decides to do her own experiment using the class data survey collected at the beginning of class on the number of hours a student takes during her Spring 2019 BUSI 2305 course. The data file has a total number of 54 students where the average is 10.8 with a standard deviation of 3.15. She sets out to collect the mean on 8 samples of 6 students. Based on this what are the total possible samples that could occur based on the population
Answer:
25827165
Step-by-step explanation:
from the question that we have here
the total population = 54 students
the sample size = 6 students
So given this information carol has to pick the total samples from the 54 students that we have here
the total ways that she has to do this
= 54 combination 6
= 54C6
= [tex]\frac{54!}{(54-6)!6!}[/tex]
= 25827165
this is the total number of possible samples that could occur given the total population of 54 students.
the mean of 200 item was 50 later on it was found that two items were wrongly taken as 92 and 8 instead of 192 and 88 find the correct mean.
Answer:
Since, mean of 200 items was 50 and number of items =200
So, mean =50
Also, we know mean = number of itemssum of items
∴50=200sum of items
Sum of items = 200×50=10000
Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88 respectively
Then misread instead Correct item
92 192 192-92=100
8 88 88-8=80
∴ Correct sum of items =10000+180=10180
∴ Correct mean = number of items/sum of items
=10180/200 =50.9
Answer:
Hello,
203.6
Step-by-step explanation:
Sum of the item first= 50*200=10000
new sum is 10000+(192-92)+(88-8)=10180
New mean=10180/200=50.9
Find the missing side lengths leave your answer as a racials simplest form
Answer:
x = 20
y = 10
Answered by Gauthmat
